FULL PAPER

Interleaved Multishot Imaging by SpatiotemporalEncoding: A Fast, Self-Referenced Method forHigh-Definition Diffusion and Functional MRI

Rita Schmidt, Amir Seginer, and Lucio Frydman*

Purpose: Single-shot imaging by spatiotemporal encoding(SPEN) can provide higher immunity to artifacts than its echo

planar imaging–based counterparts. Further improvements inresolution and signal-to-noise ratio could be made by rescind-ing the sequence’s single-scan nature. To explore this option,

an interleaved SPEN version was developed that was capableof delivering optimized images due to its use of a reference-

less correction algorithm.Methods: A characteristic element of SPEN encoding is theabsence of aliasing when its signals are undersampled along

the low-bandwidth dimension. This feature was exploited inthis study to segment a SPEN experiment into a number of

interleaved shots whose inaccuracies were automatically com-pared and corrected as part of a navigator-free image recon-struction analysis. This could account for normal phase

noises, as well as for object motions during the signalcollection.Results: The ensuing interleaved SPEN method was applied

to phantoms and human volunteers and delivered high-qualityimages even in inhomogeneous or mobile environments. Sub-

millimeter functional MRI activation maps confined to graymatter regions as well as submillimeter diffusion coefficientmaps of human brains were obtained.

Conclusion: We have developed an interleaved SPENapproach for the acquisition of high-definition images that

promises a wider range of functional and diffusion MRI appli-cations even in challenging environments. Magn Reson Med75:1935–1948, 2016. VC 2015 Wiley Periodicals, Inc.

Key words: spatiotemporal encoding; interleaved MRI; high-

definition fMRI; high-resolution ADCs; full refocusing; refer-enceless reconstruction

INTRODUCTION

Single-scan MRI techniques play important roles in func-tional, diffusion, flow, thermometry, and real-time ana-tomical studies. A key component of many of thesesubsecond applications is echo planar imaging (EPI)(1–6). One of EPI’s drawbacks stems from its sensitivity

to field and shift inhomogeneities along the low-bandwidth direction (7). Recent studies have focused onalternative single-scan methods derived from spatiotem-poral encoding (SPEN) (8), a strategy that combinesfrequency-swept pulses and gradients to image thisdimension (9). SPEN offers the possibility of using stron-ger acquisition gradients than those used in EPI, resultingin a higher immunity to field inhomogeneities (10,11). Animportant feature of SPEN is its ability to scan the low-bandwidth dimension under “fully refocused” conditions,whereby each excited spin packet experiences a full spinecho at the time of its sequential detection (12). This fur-ther increases the robustness of the scan to various sourcesof offset. A variety of sequences combining hybrid k- andSPEN-space encoding along the high- and low-bandwidthdimensions have thus been demonstrated, with advanta-geous results for functional, diffusion, anatomic, and ther-mometry applications (13–17).

Despite this potential, single-scan SPEN images maystill suffer from blurring, signal loss, and distortions.This degradation will occur, as in EPI, due to the longacquisition durations imposed by gradient slew rates andgradient strength limitations, particularly in clinicalscanners. To reduce these long acquisition times, weexplored an interleaved multishot sequence using princi-ples akin to those employed in interleaved EPI (18,19).Well-known weaknesses of multishot interleaved EPIinclude the appearance of ghosts and blurring resultingfrom phase errors between shots (20,21), instrumentalinstabilities, respiration and cardiac pulsations, or otherbulk motions (22–25). Accounting for these phase errorsrequires the acquisition of ancillary navigator scans oreven more complex forms of reference scan acquisition(26,27). Although correction methods for interleaved EPIinvolving no reference scans have also been proposed(28,29), such implementations are not always applicable.The proposed interleaved multishot SPEN approach pos-sesses a valuable advantage with regard to these meth-ods, as it can deliver an improved image free fromartifacts via a referenceless reconstruction procedure.This benefit results from SPEN’s non-Fourier nature andfrom its lack of image aliasing artifacts upon attemptingto reconstruct images from sparsely sampled data. Thisadvantage (30) has no counterpart in EPI and, as shownin this study, can correct errors stemming from the afore-mentioned instrumental and in vivo instabilities. Theoutcome is a new approach to interleaved multishotSPEN that can provide robust high-resolution images.We explored this approach using phantom studies andhuman volunteer studies, including brain functional MRI(fMRI) and diffusion experiments, multislice breast

Chemical Physics Department, Weizmann Institute of Science, Rehovot,Israel

Grant sponsor: Israel Ministry of Trade and Industry; Grant number: Kamin-Yeda Project 711237; Grant sponsor: European Research Council; Grantnumber: 246754; Grant sponsor: Federal German Ministry for Educationand Research; Grant number: DIP Collaborative Project 710907; Grantsponsor: Helen and Martin Kimmel Award for Innovative Investigation;Grant sponsor: Perlman Family Foundation.

*Correspondence to: Lucio Frydman, Chemical Physics Department, Weiz-mann Institute, 76100 Rehovot, Israel. E-mail: lucio.frydman@weizmann.ac.il

Received 16 July 2014; revised 31 March 2015; accepted 31 March 2015

DOI 10.1002/mrm.25742Published online 23 June 2015 in Wiley Online Library (wileyonlinelibrary.com).

Magnetic Resonance in Medicine 75:1935–1948 (2016)

VC 2015 Wiley Periodicals, Inc. 1935

imaging studies, and studies wherein volunteers wereasked to move between shots.

THEORY

Pulse Sequence Considerations

For the sake of simplicity, we consider first the execu-tion of a one-dimensional (1D) SPEN experiment alongthe y-axis. SPEN delivers its images by the combinedaction of a chirp pulse of rate R and duration Tenc, andof a gradient of strength Genc (31,32). These parametersare related to the experiment’s field of view (FOV)through BW ¼ RTenc ¼ gGencFOV , where BW is the chirppulse bandwidth. Such combination imparts a parabolicphase profile on the encoded spins wencðyÞ ¼aency2 þ bency þ const. For SPEN experiments based on

90 deg excitation chirp pulses (Fig. 1a) a908¼�gGencTenc

2FOV ,

b908¼gGencTenc

2 � wcsTenc

FOV ; if SPEN is based on 180 deg adia-

batic sweeps (Fig. 1b), then a1808¼�gGencTenc

FOV , b1808¼gGenc

Tenc� wcsTenc

FOV , with b180 8 including a prephasing gradient

and wcs the frequency offset.The signal acquired in a 1D SPEN MRI experiment can

be expressed as (11)

SðtÞ ¼ZFOV

2

�FOV2

rðyÞei½wencðyÞþkðtÞy �dy ; [1]

where kðtÞ ¼ gR t

0 Gacqðt0 Þdt

0describes the effects of a gradi-

ent applied during the acquisition. It has been shownbased on the stationary phase approximation that this sig-nal will be proportional to the spin density profile q(y).Image reconstruction, however, is enhanced by super-resolution (SR) methods (33–35) that improve resolutionand allow one to use lower R rates and lower gradientstrengths, thereby decreasing the overall specific absorp-tion rate (SAR). In the SR method implemented in thisstudy, the integral in Equation [1] is replaced by an expres-sion that assumes N discrete spatial points {qn}n¼1. . .N andM discrete measured points {Sm}m¼1. . .M, leading to

SðkmÞ �XNn¼1

rn

Zynþd

yn�d

ei½aency2þðbencþkmÞy �dy ¼XNn¼1

rnAmn; [2]

where yn is the voxel’s y center, 2d is the voxel’s width,and Amn are elements of a so-called SR matrix. Equation

FIG. 1. Interleaved multishot SPEN pulse sequence schemes. (a) 90 deg chirp pulse sequence involving a central slice-selective (ss)spin echo. (b) Multislice interleaved SPEN version using an initial 90 deg slice-selective excitation, a pre-encoding delay to (tuned to fully

refocused conditions as an example), a 180 deg chirp pulse, and a postacquisition hard 180 deg pulse returning all spins outside the tar-geted slice back to thermal equilibrium. (c) Acquisition trajectory in the hybrid SPEN/readout space for a four-shot interleaved acquisi-tion case, with a pair of two-shot intermediate reconstruction. When implementing functional MRI scans, uniform delays s were

introduced as illustrated in the sequences. If the BOLD-sensitizing delay s is desired >Tacq/2, to is set to 0 and a delay s � Tacq/2 isadded after the 180 deg chirp pulse. Abbreviations: cr, crusher; RF/ADC, radiofrequency and analog-to-digital conversion channels; RO,

readout; sp, spoiler

1936 Schmidt et al.

[2] can be rewritten in matrix form as S 5 Aq; the imageretrieval problem can then be solved in the N�M caseas r ¼ Að�1ÞS where Að�1Þ is a matrix required for a stablesolution. As in previous studies, we used a single-iteration algorithm based on the conjugate gradientmethod to find this matrix and solve for q, including aGaussian weighting of A’s columns before the calcula-tion of this inverse matrix (30,33).

These 1D principles can be extended to a single-scantwo-dimensional (2D) imaging setting by considering ahybrid SPEN sequence (9–11) that combines a k-spaceacquisition in the readout direction, with SPEN in thelow-bandwidth direction. In this case, the final spin den-sity will be a matrix qnq, where n¼ 1. . .N indexes thepoints along the SPEN dimension and q 5 1. . .Q denotespoints in the readout direction (Fig. 1). As happens forEPI (19), this single-shot sequence can be furtherextended into an interleaved multishot format endowedwith a higher definition, better sensitivity, and improvedrobustness against frequency offsets along the low-bandwidth dimension (20). In the EPI case, interleavedacquisitions are compromised by a need for corecordingancillary calibrating scans for their processing, thusavoiding increased Fourier artifacts. SPEN methods cir-cumvent this penalty due to their avoidance of Fourierprocessing along the low-bandwidth dimension. Toappreciate this feature, consider a multishot SPENexperiment entailing a repeat of Nshot interleaved scansthat differ by the addition—prior to their respectiveacquisitions—of a proper gradient-driven displacementalong their low-bandwidth directions. Figure 1c presentsthe fashion in which this multishot array can be recon-structed into a unified data set for Nshot¼ 4. Assumingthat each one of these Nshot acquisitions entails M pointsalong their SPEN axes, the result will be an array ofSPEN data sets composed of Mtotal 5 MxNshot points.Each SPEN shot will now involve a larger blipped gradi-

ent of area Dkacq ¼ lenc �gGencTenc

Mtotal=Nshotand be preceded by a vari-

able “k-kick” kl ¼ lenc �gGencTenc

Mtotalðl � 1Þ (l¼ 1. . .Nshot), where

kenc depends on whether the encoding was implementedby a 90 deg or 180 deg frequency sweep: l908 ¼ 1 andl1808 ¼ 2. The interleaved data rearrangement describedin Figure 1c thus gives sufficient information to recon-struct the spin density from these M points, even if eachscan’s acquisition time was reduced by Nshot and concur-rently shorter pulse durations were required for achiev-ing the fully refocused conditions Tacq¼ lencTenc (13,36).

Referenceless Reconstruction of Interleaved SPEN Data

In contrast to EPI, where Dk ¼ 2pFOV, the SPEN Dkacq just

introduced is proportional to the FOV. This follows fromthe stationary phase approximation and from Equation[1]: Dkacq ¼ �2aenc

FOVM . Hence, if one compares an EPI

experiment in which k-space data set is undersampledby a factor of Nshot with regard to a comparable SPENdata acquisition, EPI’s Dk step increase will result in areduction of the image’s FOV to FOV/Nshot and producean aliasing effect. In contrast, a similar step increase inSPEN will keep the FOV constant but increase the sam-pling intervals of the stationary point (i.e., reduce the

image’s resolution). In other words, interleaved SPENallows one to shorten each scan’s duration at theexpense of decreasing spatial resolutions, but not at thecost of aliasing. A four-shot interleaved SPEN acquisi-tion, for instance, could have the data from each shotreconstructed separately to yield images with the sameFOV as a full SPEN acquisition but with spatial resolu-tions reduced by a factor of four. Moreover, pairs ofscans in this {1,2,3,4} series could be jointly coprocessedas {1,3} and {2,4} (Fig. 1c) to yield two midresolutionimages with double the spatial resolution, and an imagewith maximum resolution could be reconstructed bycoprocessing all four shots. This hierarchical reconstruc-tion can be further extended in a “sliding window” fash-ion (Fig. 2) to yield high-definition images withoutpaying the full temporal acquisition penalty.

Absence of aliasing in undersampled SPEN imagesenables a referenceless joint reconstruction of all scansbased on an estimation of the phase errors among theinterleaved data. The principle of referenceless SPENreconstruction was demonstrated for the coprocessing ofsingle-scan even-and-odd data sets via a common SRprocedure (30); in this study, we adopted and extendedthese principles to the coreconstruction of multipleinterleaved SPEN acquisitions without ancillary

FIG. 2. Referenceless processing algorithm for the reconstruction

of interleaved multishot SPEN data with corrections for the phaseerrors and motions exemplified for an experimental four-shotacquisition case. The relationships between the various signal and

spin density S- and q-matrices are further described in the text; inthe present example, all of these matrices are presented after

Fourier transformation along the readout direction, and processesindicate actions taken along the SPEN dimension.

Referenceless Interleaved SPEN MRI 1937

navigators. Toward this end the signal of each shot,

fSðlÞgl¼1;Nshotis used to reconstruct a low-resolution image

frðlÞnq ¼ ½AðlÞmn��1SðlÞmqgl¼1;Nshot

, where n¼ 1. . .N/Nshot and

m¼ 1. . .M 5 Mtotal/Nshot index the points along SPEN’simage and digitized dimensions, and q 5 1. . .Q are points

along the readout direction. Here, AðlÞmn represents the

pertinent SR matrix for shot l (including the relevant kl

shifts for each of the shots), defined similarly as in Equa-tion [2] by

AðlÞmn ¼Zynþd

yn�d

ei aency2þ bencþklþDkacq�ðm�1Þð Þ½ �dy : [3]

In an ideal case, one would expect to obtain nearlyidentical frðlÞnqgl¼1;Nshot

low-resolution images for all thescans involved in the multishot acquisition. However,due to intermittent errors between shots, phases will beadded to the solutions, and r

ðlÞnq reconstructed from the

various shots will differ. To estimate these phase errorsand achieve a consistent set of data, we correct eachshot’s low-resolution images as

rðlÞnq

rðl¼1Þnq

¼ eifnq ; rðlÞ;corrnq ¼ e�ifnq rðlÞnq: [4]

The justification for this correction is as described bySeginer et al. (30) for the referenceless coprocessing ofeven/odd lines in single-shot SPEN acquisitions. As in thestudy by Seginer et al., it is practical to generate the phasemaps unq corresponding to each of these images as a gen-eral 2D fit of the experimental phase differences based on asecond-order polynomial expansion. With the correspond-ing correction applied to all images, a set of undersampledsignals SðlÞcorr ¼ A

ðlÞmnr

ðlÞcorrnq (where in fact S(1),corr¼S(1)) is

back calculated. Sampled data points thus corrected can becombined again in an interleaved fashion as

Scorr¼

Sðl¼1Þ;corr1;1 . . . S

ðl¼1Þ;corr1;Q

Sðl¼2Þ;corr1;1 � � � S

ðl¼2Þ;corr1;Q

�

Sðl¼NshotsÞ;corr1;1 � � � S

ðl¼NshotsÞ;corr1;Q

�

Sðl¼1Þ;corrMtotal=Nshots

;1 � � � Sðl¼2Þ;corrMtotal=Nshots

;Q

Sðl¼2Þ;corrMtotal=Nshots

;1 � � � Sðl¼2Þ;corrMtotal=Nshots

;Q

�

Sðl¼NshotsÞ;corrMtotal=Nshots

;1 � � � Sðl¼NshotsÞ;corrMtotal=Nshots

;Q

266666666666666666666666666666666664

377777777777777777777777777777777775

: [5]

Coprocessing of this augmented matrix then yields ahigh-resolution image r

fullnq from r

fullnq ¼ ½Afull

mn ��1Scorrmq , with

n, q, and m as before. Although theoretically this

procedure should be sufficient, we found that, in prac-tice, possible inaccuracies arising from the small numberof image points collected in each shot make it subopti-mal. To improve the SR solution’s stability, we performthe frl

nq ¼ ½AðlÞmn��1S

ðlÞmqgl¼1;Nshot

inversion in an iterativeloop, each time combining a pair of images to generateprogressively higher levels of resolution. For example, inthe four-shot case (Fig. 2), one would first coprocess shot1 with shot 3 and shot 2 with shot 4 to correct for thephase error within each pair, generating a pair of midreso-lution images. The phase-balancing procedure wouldthen be repeated for these two midresolved images to cor-rect for the phase error between them; this set of images isthen jointly coprocessed to obtain the final, highest-resolution image. With such a procedure, the number ofpoints participating in the phase error correction becomeshigher as the iteration number increases, improving thecorrection’s accuracy. For the case where the number ofshots is a power of two (ie, Nshot¼ 2p), the total number ofiterations is thus p 1 1, including a first iteration that cor-rects the even/odd phase errors within each shot (e.g., forfour interleaves, the number of iterations would be three).

A potentially important source of artifacts in seg-mented acquisitions stems from movements in theimaged object. In k-encoded methods like EPI, motionleads to phase errors between the various images, pri-marily along the phase-encoded direction. In SPEN, onecan use the previously mentioned absence of aliasingeffects to correct common cases of in-plane rigid motionswithout the use of ancillary navigators. The solution ofeach shot’s equation r

ðlÞnq ¼ ½AðlÞmn��1SðlÞ would then deliver

low-resolution images of the shifted object; these can becoregistered, for instance by applying canonical rotation(R̂) and translation (R

!0) transformations: r

ðlÞ;registerednq ð r!nqÞ

¼ rðlÞnqðR̂ r!nq þ R

!0Þ (22). With these corrections, it

becomes possible to recalculate back images of the tar-geted object in a common, “static” frame, SðlÞ;registered

¼ AðlÞmnr

ðlÞ;registerednq Once individual images are coregis-

tered, the previously described phase error correctionprocedure can be used again. The effect of the rotationand translation transformations will result in in-plane,spatially dependent phase shifts that in all likelihoodwill be different from the initial phase error terms. Thesenew terms will still be fully compatible with an in-plane2D phase correction of the kind shown in Figure 2; theadditional coregistration procedure can thus be added asintermediate step between the previously describedphase correction iterations.

Signal-to-Noise Ratio Considerations

Before discussing signal-to-noise ratio (SNR) in the caseof multishot SPEN, we briefly recapitulate the main SNRfeatures of single-shot SPEN with regard to single-shotEPI. As originally shown by Tal and Frydman (12),SPEN’s SNR is 1 ffiffiffi

Np= times lower than that of k-space

encoded MRI if pulse parameters are chosen so that amagnitude calculation of the SPEN signal willrepresent the spin density with identical range andresolution—a kind of SPEN acquisition that demandslencBW � Tenc ¼ N2 (in this case, N¼M). However, SRreconstruction algorithms allow one to choose lower

1938 Schmidt et al.

encoding BW bandwidths without sacrificing resolution,thereby improving SPEN’s SNR. In such cases, and asdiscussed in detail by Ben-Eliezer et al. (37), the ratiobetween the SNR of SPEN and of EPI acquisitions will

becomeffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

MlencBW �Tenc

qas illustrated analytically and with

numerical simulations, this ratio can be made virtuallyunity for suitably set single-shot acquisitions. Withregard to multishot acquisitions, as happens to be thecase when executing EPI in an interleaved fashion, inter-leaved SPEN exhibits an improved per-scan SNR whencompared with averaged single-shot counterparts withthe same final spatial resolution. Taking into account T2

weightings and using a notation similar to that describedby Ben-Eliezer et al., the SNR can be summarized for

interleaved SPEN as DyDxffiffiffiffiffiffiQNsw

q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiMtotal

lencBW �Tenc

q� e�TEm=T2 .

Here, sw is the readout spectral width, Dx and Dy are thefinal spatial resolutions along the read-out and SPENdirections, Q and N are the total number of pointsacquired along the readout and spatiotemporal encodingdirections, BW � Tenc is the time-bandwidth product ofthe chirp pulse, and kenc¼ 1 or 2 as introduced above.

Similar to the single-shot case, theffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Mtotal

lencBW �Tenc

qratio

reflects SPEN’s generally lower SNR versus EPI due toits direct (as opposed to reciprocal) space samplingnature (12,37). The TEm mentioned in the SPEN SNRexpression is the echo time (TE) for each of the acquiredpoints, which falls in the 0<TEm< 2Tacq range for the90 deg chirp pulse sequence and in Tacq /2�TEm� 2Tacq

for the 180 deg chirp pulse sequence (with both casesassumed recorded under fully refocused conditions).Because acquiring a high-resolution image within asingle-shot requires longer Tenc and TEm times comparedwith the values needed for an interleaved counterpart,this expression predicts that the SNR improvementsbrought about by interleaving can be substantial. As ininterleaved EPI methods, this shortening in the encodingand acquisition times may also enable one to reduce therepetition time (TR). Although this was not done in ourphantom-based SNR comparisons, should the TR beshortened, then potential saturation effects or the possi-bility of changing the optimized excitation angle shouldbe factored into the SNR considerations (38). The Appen-dix describes some of these TE- and TR-related SNReffects as calculated for a set of prototypical T1 and T2 val-ues. These calculations reveal that the SNR gain achieva-ble by multishot acquisitions due to shorter TEs can besubstantial; for example, four-shot SPEN images collectedover a total scan time of 3 s (ie, TR¼ 0.75 s) using a TErange of 40–100 ms could yield SNR improvements rang-ing between 1 and 10 depending on location and the exactrelaxation parameters assumed, despite the fact that reso-lution is being improved by a factor of 4. Moreover, theshortened encoding/acquisition times also increaseimmunity against B0 inhomogeneity, leading to a dramaticpotential to improve an image’s quality (e.g., see Fig. 4).

METHODS

The principles just described were explored with a seriesof phantom tests aimed at examining the benefits that

the interleaved procedure could deliver in relativelyinhomogeneous B0 environments as well as in the pres-ence of motions. The phase and motion correction algo-rithms were also explored in vivo on healthy volunteers,including high-definition fMRI studies of a motor para-digm and diffusion-weighted brain sagittal studies. Allthese experiments were implemented on a 3T SiemensTIM TRIO scanner (Siemens Healthcare, Erlangen:Germany) using custom-written codes based on thesequences in Figures 1a and 1b. The ensuing imageswere reconstructed using custom-written MATLAB pack-ages (MathWorks, Natick, Massachusetts, USA) thatincluded the rearrangements and the algorithmsdescribed in Figure 2, as well as Fourier transformationalong the k-space readout direction. (The acquisition andreconstruction codes are available upon request.)

One set of experiments was performed using an Ameri-can College of Radiology MRI phantom to demonstratethe SNR and resolution improvement arising from inter-leaved SPEN acquisitions. Another set of phantomexperiments was conducted to examine the performanceof interleaved SPEN and EPI acquisitions in inhomoge-neous B0 environments using an orange and bananasetup as an example.

Human volunteer imaging studies were approved bythe Internal Review Board of the Wolfson Medical Center(Holon, Israel) and were performed after obtaininginformed consent. One such set of experiments centeredon fMRI brain scans using a four-channel head coil withT�2 weighting (ie, with SPEN’s fully refocused conditionsbroken by the addition of a pre-acquisition delay t),introducing a T�2 weighting akin to that in gradient echoEPI (GE-EPI). The paradigm of these experiments was amotor stimulus involving the uninterrupted tapping ofall fingers (tapping frequency of �2 Hz) in either theright or the left hand for 30 s each (39); five pairs ofsuch stimuli blocks were conducted for a total studyduration of 5 min. The functional experiments wererepeated using both single-shot GE-EPI and interleavedfour-shot SPEN. The GE-EPI echo time as well as theequivalent delay responsible for the T�2 weighting in thefour-shot SPEN experiments were set to t¼30 ms. It isimportant to stress that in the case of SPEN, this delaybreaks an otherwise fully refocused condition that wouldfree signals from T�2 effects. Therefore, t yielded aposition-independent BOLD weighting, without whichno activation could be detected under the field and func-tional paradigms hereby assayed. In order to keep a con-stant scan time per (final) image, the TR of the four-shotSPEN was 0.75 s, and the flip angle was 60 deg. Theseexperiments were repeated on four volunteers (three ofwhom underwent axial experiments and a fourth whounderwent coronal experiments), and axial as well ascoronal orientations were scanned. For deriving func-tional activation, t-score maps were calculated (40) forall the axially scanned volunteers, as statistical signifi-cance of the mean signal difference in a time seriesbetween two conditions in a voxel-by-voxel basis, usinga gamma function to account for the hemodynamicresponse function (41). The average percent of signalchanges over the time course of the stimuli were calcu-lated for both SPEN and GE-EPI scans on identical

Referenceless Interleaved SPEN MRI 1939

regions chosen from the anatomical image on these sub-jects for GE-EPI and on SPEN experiments executed witha matrix of 128260 pixels (128 130 pixels for onesubject). The error bars for these activation plots reflectthe standard error observed for the region of interest overthe stimuli repetitions. These calculations were per-formed in MATLAB using custom-written software.

An additional set of interleaved SPEN brain experi-ments centered on diffusion-weighted scans (42) was col-lected in a sagittal orientation. Toward this end, themultislice sequence (Fig. 1b) was modified to includediffusion-weighting gradients. Mean ADCs wereextracted from images generated from a single, two, andfour interleaved shots after suitable calculations of theSPEN-weighted b values (43) arising from diffusionweightings applied along all orthogonal axes, with nomi-nal b values ranging from 0 to 1000 s/mm2. Comparisonsagainst single-shot spin echo EPI (SE-EPI) were alsomade; interleaved SE-EPI acquisitions were not pursueddue to poor performance. It is worth noting that in thesein vivo diffusion-weighted experiments, a high phase-wrapping was detected, which required a careful phaseunwrapping algorithm (44) to implement the reference-less procedure in Figure 2.

In addition to these brain studies, human breast imageswere collected using the sequence in Figure 1b in order toexplore the performance of multislice interleaved SPENwhen operating in heterogeneous tissue environments;these results can be found in Supporting Figure S1.

A final set of experiments involved examining thecapability of the algorithm in Figure 2 to account forphase errors associated with rigid body motions. Theseexperiments involved phantoms that were artificiallymoved along the SPEN direction and volunteers whowere requested to swivel their heads in a right-to-leftmotion throughout the course of a brain scan. To findrigid transformations that best compensate for themotion, a minimization of the (absolute) correlationsbetween intermediate images (after a rigid transforma-tion) was performed using an open-source MATLABcode (45) relying on the fminsearch function and theNelder-Mead algorithm (46). Low-resolution images thusregistered were used as an input for the phase error cor-rection algorithm as shown in Figure 2.

RESULTS

Interleaved SPEN: Phantom Experiments

Figure 3 shows representative results collected on anAmerican College of Radiology phantom, comparing theSNR of images collected with the same final resolutionusing single-scan SPEN versus two- and four-shot inter-leaved examples. The SNR improvement with increasingnumber of shots is evident, with the sensitivity of thefour-shot image is about four times higher than that ofits single-shot counterpart. These gains derive from theconsiderably shorter echo times involved in the inter-leaved SPEN with regard to single-shot acquisitions: 32ms for the four-shot SPEN versus 107 ms for the single-shot SPEN at the middle of the image. Such reductionleads to significant SNR gains, as T2 tissue values are inthe 60–120 ms range. An additional point to notice is the

reduced T2 weighting along the SPEN direction, whenimages are collected in multiple shots. Also illustrated inFigure 3 is the fact that if the same acquisition durationsare used in the single-shot and multishot schemes, ahigher resolution image will result from the latter due tothe larger number of points acquired. Further resolutionimprovements can derive from exploiting SPEN’s built-inrestricted FOV features, which can be used in the inter-leaved implementation for improving the resolution evenfurther. This is exemplified by the profiles in Figure 3h,which compares similar SPEN acquisitions collected witha full FOV and with half the FOV.

Figure 4 examines the robustness of interleaved multi-shot SPEN and EPI scans to B0 inhomogeneity. The setupincluded a banana and an orange positioned in the cen-tral FOVs, and single versus interleaved shots were com-pared seeking morphological details at a 1–2 mmresolution. Although the single-shot SPEN image wasconsiderably less distorted than its single-shot EPI coun-terpart, both failed to provide sufficient resolution—andin the case of the banana, which had a shorter T2, signalintensity was similarly insufficient. Considerableimprovements arose from acquiring four interleavedshots; still, even in this case, the EPI image showedhigher distortions than its SPEN counterpart when com-pared with their multiscan reference. It is worth notingthat the single-shot SPEN immunity to B0 inhomogeneitycould in principle be improved by increasing the chirpedpulse bandwidth; such improvement, however, wouldcome at the cost of increased SAR and reduced SNR.These compromises were alleviated upon operating in amultishot, interleaved acquisition mode.

High-Definition Functional Brain Examinations byInterleaved SPEN MRI

To further examine the potential of this method, fMRImeasurements of motor stimuli were performed usingsingle-scan SPEN and EPI, as well as interleaved SPEN.Figure 5 shows a summary of these measurements, withmagnitude images reconstructed from single-shot GE-EPI(usually considered a gold standard in this type ofexperiment) and from interleaved four-shot SPENsequences, displayed with an overlay of those pixelsshowing a t-score5. These images clearly show thatthe four-shot acquisitions delivered a higher spatial reso-lution without penalties derived from a stronger T2 or T�2weighting. The activation areas in these interleavedSPEN experiments (Fig. 5b,c) are similar to those in con-ventional GE-EPI. This performance is evidenced in boththe axial and coronal acquisitions. Figure 5e shows thepercentage of the signal change due to the stimuli inaxial scans performed by GE-EPI and by interleavedSPEN. The latter shows an increase in the signal activa-tion by �50%; this illustrates the potential of the newmethod, even if further studies are needed to assess theprecise factors contributing to such an enhancement.

It is enlightening to use this fMRI example to illustratehow the SPEN phase maps vary between individualshots, and how these are estimated and compensatedusing the new referenceless correction method. Phasemaps from a representative fMRI experiment together

1940 Schmidt et al.

with intermediate steps involved in processing inter-leaved scans into a final high-definition image can befound in Supporting Figure S2.

High-Definition Diffusion-Weighted MRI by InterleavedSPEN

In an additional exploratory study, interleaved diffusion-weighted SPEN images were recorded for a human brainalong a sagittal orientation. All these images are com-pared for b¼0 in the top row of Figure 6. Figure 6 alsoshows the mean ADC maps calculated from single-, two-,and four-shot experiments. The improvements in theimages, particularly close to air–tissue interfaces, are evi-dent with the number of increasing shots. The quantita-tive values exhibited by ADCs in all the maps are alsosimilar.

Motion Compensation in Interleaved SPEN

As mentioned, the referenceless reconstruction algorithmhas the potential to correct in-plane motion occurringbetween shots. Figure 7 shows this by presenting images

arising from phantom and brain scan experiments,whose reconstructions were implemented using the algo-rithm in Figure 2 in the absence and presence of motion.The displacements before and after the phantom/brainmovements are evident in these panels. Nonetheless, thefinal images that were reconstructed by relying on themotion correction and the referenceless reconstructionalgorithms described earlier (Fig. 7d) showed no noticea-ble blurring and were comparable with the four-shotinterleaved SPEN images that were acquired when nomovements occurred (Fig. 7e).

DISCUSSION AND CONCLUSIONS

This study examined an approach extending single-shothybrid SPEN, to multishot interleaved acquisitions. Thisoption rescinds the original method’s goal of collecting afull 2D image in one scan; on the other hand, in just afew scans, it can deliver higher resolution images thatare endowed with better SNR and are less susceptible todistortions arising from heterogeneous magnetic fields.Similar benefits had been reported previously in multi-shot acquisitions relying on EPI; as in such instances,

FIG. 3. Interleaved SPEN experiments collected on the American College of Radiology phantom. (a) Multiscan 2D profile of the phan-tom. (b–d) Single-shot (b), two-shot (c), and four-shot (d) SPEN scans collected with the same final resolution. The SNR displayed on

these images was calculated by focusing on the yellow marked region; notice as well the decreased T2 effects with increased interleav-ing. (e, f, d) Images reconstructed from a single shot (e), a pair of shots (f) and a four-shot acquisition leading to (d); all shots contained

the same number of points, and the progression illustrates the process illustrated in Figure 2. (g) Interleaved four-shot SPEN imageacquired as in (d), but with a restricted FOV leading to higher resolution. (h) Image profiles plotted along the segmented line marked onimages (a), (d), and (g); the resolution achieved for the phantom’s fine structure along this line can be seen to improve upon relying on

the restricted FOV four-shot SPEN (see Methods for further parameters). Common scan parameters: sequence in Figure 1a, FOV2424 cm2, final resolution 1.71.7 mm2, slice thickness¼4 mm. Parameters for the four-shot SPEN were: flip angle¼60 deg,

Tenc¼25 ms, Tacq¼25 ms, Genc¼0.06 G/cm, TE¼7–57 ms (depending on the position of the spins), number of acquiredpoints¼14035 per shot, and TR¼0.75 s. Parameters for the two-shot SPEN were: flip angle¼60 deg, Tenc¼50 ms, Tacq¼50 ms,Genc¼0.06 G/cm, TE¼7–107 ms, number of acquired points¼14069 per shot, and TR¼0.75 s. Parameters for the single-shot SPEN

were: flip angle¼90 deg, Tenc¼100 ms, Tacq¼100 ms, Genc¼0.05 G/cm, TE¼7–207 ms, number of acquired points 140140, andTR¼3 s. In addition a restricted FOV, four-shot SPEN scans were run with the same number of acquired points as for the full FOV, thus

further increasing the resolution. This scan was run with the following parameters: FOV¼2412 cm2, final resolution¼1.70.85 mm2,flip angle¼60 deg, Tenc¼25 ms, Tacq¼25 ms, Genc¼0.12 G/cm, TE¼7–57 ms, the number of acquired points 14035 per shot, andTR¼750 ms. Reference spin echo multiscan parameters were: resolution¼0.930.93 mm2, TE¼72 ms, TR¼1.5 s, number of scan

averages¼2, and total scan duration¼35 s. The striated appearance on some of the images arises from the noniterative method thatwas chosen for the SR reconstruction and is not related to the use of scan interleaving. Alternative reconstruction methods (34,35)

appear to be devoid of such minor artifacts.

Referenceless Interleaved SPEN MRI 1941

much of the sensitivity and robustness gains of multishotSPEN derive from the use of progressively shorter echoesand acquisitions. In the case of interleaved multishotEPI, these potential benefits are often offset by the ensu-ing experiment’s sensitivity to phase errors betweenshots, calling for a need for additional navigator scans orfor double-FOV 2D reference scans. By contrast, anattractive feature of the interleaved multishot SPENapproach is the fact that all the information required forperforming its phase error correction is “built into” theindividual images that are combined. This allows one toreap the full benefits of interleaved schemes while obvi-ating the need for collecting extra reference acquisitions.The robustness of the referenceless algorithm describedherein is evidenced by its ability to correct even for thelarge phase errors arising when an object is purposefullymoved between shots. Nonetheless, strip-like artifactsare visible in some of the illustrated images. These appearrelated to challenges in performing a perfect phase correc-tion by the self-referenced SR algorithm; further researchincorporating regularization methods as well as B0 inho-mogeneity corrections into the algorithm might alleviatethese artifacts (47). In the present study, a somewhat sim-plistic approach was used to implement the individualimages joint coregistration; more involved algorithms con-sidering out-of-plane motions as well plastic deformationsof the object could also be included (48). Accounting forsuch motion-derived distortions was found secondary in

applications such as the fMRI study presented in Figure5, where spontaneous instabilities dominated the inter-mittent phase variations between shots; however, theywere relevant when analyzing other tissues in whichinvoluntary motion is unavoidable (e.g., breast).

An important consideration in SPEN relates to theexperiment’s SAR, which tends to be higher than in EPI-based counterparts. To consider how SAR changes inmultishot acquisitions, we recall that in SPEN sequen-ces, immunity to B0 inhomogeneities depends on the

MlencBW �Tenc

ratio; therefore, when comparing SAR in single-shot versus multishot SPEN acquisitions, it is reasonableto keep this ratio constant while using parameters fulfill-ing the fully refocused condition. Because the SAR of apulse is proportional to

RjB1j2 dt=TR (where TR is the

repetition time) and for a chirp pulse B1 /ffiffiffiffiRp

(12), itfollows that SAR/BW �Tenc=

TR . This means that in multishotSPEN experiments, where the duration of the excitationand acquisition periods is reduced while the chirp’s BWis kept constant, the SAR of each interleaved shot willbe lower than that of a single scan collected at the sameTR. On the other hand, if one were to use a repetitiontime of TR/Nshot for the multishot SPEN, the SAR pertotal image would become the same as in the single-shotacquisition. Nonetheless, SAR limitations remain, partic-ularly when considering a multislice scheme such as theone introduced in Figure 1b. While interleaved multi-slice brain imaging examinations can be performed with

FIG. 4. Comparison of SE-EPI with SPEN in inhomogeneous field environments using a fruit setup with a banana and an orange. (a) Ref-

erence multiscan image. (b) Single-shot EPI image. (c) Single-shot SPEN image. (d) Interleaved four-shot SE-EPI image. (e) Interleavedfour-shot SPEN image. Common scan parameters: FOV¼2222 cm2, final resolution¼1.71.7 mm2, slice thickness¼5 mm. The four-shot SPEN used the sequence in Figure 1a with a flip angle¼60 deg, Tenc¼24 ms, Tacq¼24 ms, Genc¼0.05 G/cm, TE¼7–55 ms, num-

ber of acquired points per shot¼12833, and TR¼0.75 s. Parameters for the single-shot SPEN were: flip angle¼90 deg, Tenc¼88ms, Tacq¼88 ms, Genc¼0.04 G/cm, TE¼7–186 ms, number of acquired points¼128128, and TR¼3 s. Parameters for the four-shot

EPI were: flip angle¼60 deg, Tacq¼24 ms, TE¼30 ms, number of acquired points per shot¼12833, and TR¼0.75 s. Parameters forthe single-shot EPI were: flip angle¼90 deg, Tacq¼88 ms, TE¼94 ms, number of acquired points¼128128, and TR¼3 s. Referencespin echo multiscan acquisitions were also collected using the following parameters: resolution¼0.930.93 mm2, TE¼72 ms, TR¼1.5

s, number of scan averages¼2, and total scan duration¼35 s.

1942 Schmidt et al.

SPEN, current implementations are restricted to theacquisition of approximately 12 slices using TR¼ 3 s(Fig. 8). Acquisition of more slices is also possible at theexpense of reducing the bandwidth of the encodingpulse (and hence risking an increase in the susceptibilitydistortions). Further research to improve interleavedSPEN’s multislicing capabilities, for example using 2Dpulses for simultaneous slice selection and spatiotempo-ral encoding (49), are in progress.

To evaluate the potential benefits derived from theinterleaved procedure, two in vivo experiments that nor-mally rely on EPI sequences were examined. Oneinvolved functional MRI measurements, and its aim wasdiscerning the benefits that interleaved SPEN could pro-vide in terms of image definition. Though simple, robust,and immune to motions, this approach may not alwaysbe suitable, as when the stimulus being followed con-sists of rapidly recurring cycles that are shorter than theduration required by the interleaved acquisitions. It isimportant to note that in SPEN-based implementationsof fMRI and by variance to EPI, the image contrasts maydiffer for different spatial location. In the present study,T2 weightings were spatially dependent, yet given the

negligible contributions that T2 effects had on theobserved BOLD activation (essentially no activation couldbe observed upon working under fully refocused condi-tions for which T�2 effects were cancelled), this did notintroduce a severe functional penalty. The dominantBOLD contribution in the present study arose from break-ing the fully refocused conditions (Tacq¼ lencTenc) by theintroduction of a constant delay t; this in turn afforded auniform spatially sensitivity with regard to T�2, which asmentioned was the main source of the BOLD effectsobserved in these experiments. On the other hand,constant-time implementations of interleaved SPEN suchas RASER (14,15) could provide uniform spatial contrastversus T2 and T�2, provided that a constant T�2-encodingdelay like the one used in this study is introduced. Othertiming schemes can be conceived wherein neither T�2 norT2 weights are spatially uniform. A full analysis involvingthese various fMRI scanning alternatives when imple-mented under the high-definition conditions illustratedin Figure 5 is in progress.

A second application examined the potential of fullyrefocused interleaved SPEN MRI for retrieving high-resolution diffusion-weighted images. While requiring

FIG. 5. fMRI results obtained upon applying finger tapping motor stimuli and monitoring with single-shot GE-EPI and interleaved four-

shot SPEN. (a–d): Axially oriented experiments. (f–h): Coronal slice experiments. (a) Single-shot GE EPI scan acquisition with 8080pixels. (b) Interleaved SPEN acquisition with 128132 pixels. (c) Interleaved four-shot SPEN acquisition with 128260 pixels. (d) Axialanatomical image and magnifications showing the t-score maps overlay and, in yellow, the contour of an activated area that accurately

follows the fine structure of the underlying gray matter anatomy, which was used for estimating the average percent signal changes in(e). (e) Percent signal activation for regions shown in yellow in (d). Three subjects underwent GE-EPI and 128260-pixel SPEN experi-

ments and one subject underwent 128132-pixel SPEN; the standard errors in these plots were 0.55% for SPEN with 260 points,0.40% for SPEN with 130 points, and 0.43% for GE-EPI (standard errors were calculated for the pixels in the region shown in yellow,and in equivalent regions in other subjects). (f–h) Analogous data, but for coronal experiments. The common scan parameters for these

experiments were: FOV¼2222 cm2 and slice thickness¼5 mm. The single-shot GE-EPI parameters were: resolu-tion¼2.752.75 mm2, flip angle¼90 deg, Tacq¼56 ms, TE¼30 ms, number of acquired points¼8080, and TR¼3 s. An interleavedset of four-shot SPEN experiments was also performed using the multislice 180 deg pulse-based sequence in Figure 1b with the follow-

ing parameters: resolution¼1.71.7 mm2, flip angle¼60 deg, Tenc¼12 ms, Tacq¼24 ms, Genc¼0.03 G/cm, TE¼44–68 ms, t¼30 ms,number of acquired points per shot¼12833, and TR¼0.75 s. A second set relied on the same sequence but employed higher resolu-

tion parameters: resolution¼1.70.85 mm2, flip angle¼60 deg, Tenc¼24 ms, Tacq¼48 ms, Genc¼0.06 G/cm, TE¼56–104 ms, t¼30ms, number of acquired points per shot¼12865, and TR¼0.75 s. For the relatively thick slices examined and large activation regionsfound, repeated examinations revealed that motional errors were not a particular concern in these experiments, thus they were not

explicitly accounted for. Notice that due to differences in T2 weighting, the images in Figures 5b and 5c have different contrasts and dif-fer from the GE-EPI image containing mostly T�2-weighted contrast.

Referenceless Interleaved SPEN MRI 1943

FIG. 6. Diffusion-weighted brain imaging results illustrating the b¼0 images arising from interleaved single-shot and multishot SPENand EPI (top row), and the accompanying ADC maps resulting from multiple b-valued acquisitions collected on a single slice. (a) Refer-ence multiscan image. (b) Low-resolution magnitude SPEN image reconstructed from a single scan. (c) Midresolution SPEN image

reconstructed from two interleaved shots. (d) Four-shot interleaved SPEN image. (e) Single-shot SE-EPI imaging data. Interleaved SPENparameters were: FOV¼2424 cm2, slice thickness¼5 mm, Nshot¼4, resolution¼1.870.9 mm2, flip angle¼60 deg, Tenc¼23 ms,Tacq¼45 ms, Genc¼0.05 G/cm, TE¼101–147 ms, number of acquired points per shot¼12865, and TR¼0.75 s. SE-EPI scan param-

eters were: FOV¼2424 cm2, slice thickness¼5 mm, resolution¼1.871.87 mm2, flip angle¼90 deg, Tacq¼90 ms, TE¼131 ms,number of acquired points¼128128, and TR¼3 s. A spin echo multiscan reference was also acquired with: resolu-

tion¼0.60.6 mm2, TE¼72 ms, TR¼1.5 s, average number of scans¼2, and total scan duration¼35 s. Indicated underneath eachexperiment are average ADC values obtained by each method for four generic regions defined in (e).

FIG. 7. Interleaved SPEN acquisitions incorporating the referenceless algorithm and a simple motion correction provision. Top row:Images arising from a manually moved phantom. Bottom row: Brain images arising from a volunteer who was asked to move his head

side-to-side. (a) Reference multiscan image. (b, c) Separate initial and final shots collected as part of the interleaved SPEN set. Thedashed yellow line highlights the extent of the movement. (d) Final interleaved image reconstructed in the case of movement from fourscans. (e) Four-shot SPEN image reconstructed for a static case. Scanning parameters for these phantom motion experiments involved

the SPEN sequence in Figure 1a with Nshot¼4, FOV¼1616 cm2, final resolution¼1.21.2 mm2, slice thickness¼5 mm, flipangle¼60 deg, Tenc¼30 ms, Tacq¼30 ms, Genc¼0.1 G/cm, TE¼7–67 ms, number of acquired points per shot¼12833, and

TR¼0.75 s. Multiscan spin echo images were also collected as reference with resolution¼0.930.93 mm2, TE¼72 ms, TR¼1.5 s, 2scan averages, total scan duration¼35 s. The parameters for the human brain in-plane rotations were: Nshot¼4, FOV¼2424 cm2,final resolution¼1.90.9 mm2, slice thickness¼5 mm, flip angle¼60 deg, Tenc¼24 ms, Tacq¼24 ms, Genc¼0.03 G/cm, TE¼7–55 ms,

number of acquired points per shot¼12865, and TR¼0.75 s. The reference multiscan parameters in this case were: resolu-tion¼11 mm2, flip angle¼9 deg, TE¼3 ms, TR¼2.3 s, and total scan duration¼4 min.

some additional calculations with regard to their moreusual k-based counterparts for deriving the exact b val-ues needed (42), the results arising from these diffusion-weighted experiments are among the most promisingaspects we envision for this interleaving method. Indeed,the ADC maps that were obtained yielded distributionsthat are quantitatively similar to their single-shot SE-EPIor SPEN counterparts, but with a considerably higherspatial resolution. This makes these experiments particu-larly promising alternatives for high-definition DTI orHARDI fiber tracking studies based on diffusion-weighted data (50,51), assuming that dense three-dimensional coverage can be provided. This is actuallywithin the realm of the pulse sequence introduced inFigure 1b; Supporting Figure S1 presents multisliceresults conducted using such schemes, and interleavedDTI SPEN studies will be presented in an upcomingpublication. Additional potential in vivo applications ofthis new fast form of imaging, including studies offlow and real-time motions as well as the incorporationof an additional spectral dimension, are currently understudy.

APPENDIX

In addition to the formulations presented in the Theorysection based on Ben-Eliezer et al. (37), this Appendix

presents SNR aspects centering on 1) the effects of inter-leaving multishot acquisitions aiming to deliver similardata as a single-shot counterpart as a function of variableTRs and TEs for a variety of prototypical tissue T1 andT2 values and 2) potential blurring effects due to motionbetween the shots that could arise in interleaved SPENacquisitions if not processed with the self-referenced SRalgorithms described in this study.

SNR in multishot acquisitions can benefit from the sig-nificantly shortened echo times involved (21). This willprovide higher immunity to B0 inhomogeneities, as wellas reduced T2-derived losses that will usually overcom-pensate the SNR penalties associated to the interleavedscan’s higher resolution. Nonetheless, some experiments(e.g., fMRI) might also seek to shorten the TR of the inter-leaved acquisitions to keep the total image collection timeas short as in a single-shot imaging procedure. In suchcases, the T2-derived SNR gains achieved by shorter TEswill be partially reduced by saturation effects. In order toestimate how these various factors will affect interleavedSPEN’s SNR, signals versus TE and TR were calculatedfor a range of relaxation parameters prototypical of grayand white matter tissues [T1¼ 1.3 s, T2¼ 80 ms for the for-mer; T1¼ 0.8 s, T2¼ 110 ms for the latter (52)]. Figure A1shows signal ratio maps for four-shot versus single-shotimage acquisitions estimated from the spin echo steady-state signal intensity (53)

FIG. 8. Multislice four-shot SPEN brain images collected using the sequence illustrated in Figure 1b. Scan parameters were: number ofslices¼12, resolution¼1.90.9 mm2, flip angle¼90 deg, Tenc¼24 ms, Tacq¼48 ms, Genc¼0.06 G/cm, TE¼30–78 ms, t¼0 ms, num-

ber of acquired points per shot¼12865, and TR¼3 s.

Referenceless Interleaved SPEN MRI 1945

FIG. A1. Contour plots of the signal intensity ratios expected for four-shot interleaved (S2) and single-shot SPEN (S1) acquisitions, for avariety of TE and TR values. In a usual SPEN experiment, TE values (ie, T2 weightings) will span the indicated range (20–100 ms), withthe interleaved acquisition TEs being approximately four times shorter than their single-shot counterparts. As for TR, this was fixed at 3

s for the single-shot acquisition. The bottom axis (0.5 s�TR�3 s) indicates the penalties introduced in the four-shot acquisition upondecreasing TRs. Left: Calculations for prototypical gray matter T1¼1.3 s, T2¼80 ms values. Right: Idem for white matter (T1¼0.8 s,T2¼110 ms). Contour lines are added for signal ratios equal 1, 1.5, 2, and 5 in cyan, yellow, magenta, and red.

FIG. A2. Expected effects of different kinds of intershot movements. Left: Two-shot interleaved EPI performed with Cartesian sampling.Center: Two-shot interleaved EPI performed with center-out spiral sampling. Right: The interleaved SPEN sampling/processing intro-

duced in this study. Motions included 2- and 5-mm translations along the low-bandwidth (phase-encoding for EPI and spatiotemporal-encoding direction for SPEN) dimensions, as well as a 5 deg in-plane rotation. The input used for these simulations is the T1-weightedbrain image shown in the upper left corner.

1946 Schmidt et al.

Ssteady�state ¼ M0 � sinðuÞ � e�TE=T2

� ½1þ e�TR=T1 � 2eð�TR=T1þTR=2T1 Þ�

½1þ e�TR=T1 � cosðuÞ� ; [A1]

where M0 is the initial magnetization and h is the flipangle. The maps in Figure A1 show that in the relevantrange of 40�TE�100 ms and for a TR¼ 0.75 s as usedin our experiments, the (spatially dependent) signalimprovements will range between 2 and 20 for gray mat-ter and between 2 and 9 for white matter (flip angles inthese simulations were kept fixed to reduce the amountof variables changed simultaneously).

A second image-quality topic to consider in inter-leaved experiments relates to the potential artifacts thatmay arise due to motion between the shots. Cartesian-encoded EPI experiments will then evidence docu-mented ghosting artifacts (22–25); if a spiral k-spaceencoding is used, these artifacts will be minimized andblurring effects will occur (54). If no precautions aretaken, simulations reveal that—as in the latter spiral EPIcase—interleaved multishot Cartesian SPEN acquisitionswill be free from ghosting artifacts but will be subject toblurring (Fig. A2). On the other hand, if in these multi-shot SPEN experiments the segments are compatibilizedby the self-referenced procedure introduced in this studyprior to their SR reconstruction, these blurring effects arelargely attenuated and all movement effects virtuallyeliminated. Overall, global phase errors occurringbetween shots due to in-plane motion can be well cor-rected by the algorithm; through-plane movements arenot explicitly addressed by the algorithm, although wefind that these are partially compensated when small,and their main effect is inducing a constant phase error(eg, due to inhomogeneity-induced B0 changes).

ACKNOWLEDGMENTS

We thank Sagit Shushan (Wolfson Medical Center), EdnaHaran, and the Weizmann MRI technician team for assis-tance in the human imaging scans.

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SUPPORTING INFORMATION

Additional Supporting Information may be found in the online version ofthis article.

Figure S1. Multislice breast volunteer imaging comparing four-shot inter-leaved SE-EPI and SPEN acquisitions for seven slices chosen as well asfor a reference multiscan acquisition. Both the EPI and the SPEN experi-ments were executed with fat suppression; the latter set exploited SPEN’szooming abilities along the low-bandwidth (vertical) dimension. InterleavedSPEN parameters were as follows: FOV 5 28 3 14 cm2, slice thick-ness 5 5 mm, Nshot 5 4, resolution 5 1.7 3 0.85 mm2, flip angle 5 60 8,Tenc 5 15 ms, Tacq 5 30 ms, Genc 5 0.05 G/cm, TE 5 40–70 ms, number ofacquired points per shot 5 160 3 41, and TR 5 3 s. Interleaved four-shotEPI parameters: FOV 5 28 3 28 cm2, slice thickness 5 5 mm, Nshot 5 4, reso-lution 5 1.45 3 1.45 mm2, flip angle 5 60 8, G/cm, TE 5 44 ms, number ofacquired points per shot 5 192 3 49, and TR 5 3 s. A spin echo multiscanreference was also acquired with resolution 5 1.4 3 1.4 mm2, TE 5 72 ms,TR 5 1.5 s, scans averaged 5 2, total scan duration 5 35 s.Figure S2. Interleaved multishot SPEN imaging (collected with T�2 weightingfor the sake of eventual fMRI), acquired for the same slice of a brain volun-teer in four independent sets of experiments. For each set of experiments,data rows show the following data: magnitude images of the four individualshots; phase differences Du between two pairs –{1,3} and {2,4}– of consec-utive shots; two midresolution images arising for each of these pairs uponperforming the procedure in Figure 2; the phase differences between thesemidresolution images; and the final image coming from the latter’s jointprocessing. The phase maps were fitted by a second-order polynomial andare shown multiplied by a mask to filter out noisy areas. Notice the rela-tively random behavior of these phase maps for individual experimentalsets.

1948 Schmidt et al.